Social media platforms shape public discourse through two fundamental design choices that naturally co-occur in any field investigation: platform architecture, which defines what types of actors exist and how they interact, and recommendation algorithm, which determines what content is surfaced to users. Using agent-based simulation, we orthogonally manipulate both factors, exploring four prototypical architectures -- tree (e.g., Reddit), layered hierarchy (e.g., Facebook), network (e.g., Twitter), and complete graph (e.g., TikTok) -- and two algorithms: chronological (LIFO) and popularity-based (Hot). Drawing on prior theory that identifies and ranks canonical system architectures in terms of their flexibility we hypothesize that algorithmic effects on information spread and quality should be largest on the most flexible platforms and smallest on the most constrained ones. We find strong confirmation of this prediction. On tree-like platforms like Reddit, the algorithm has no detectable effect on information spread and quality. On layered hierarchies and networks like Facebook and Twitter, respectively, the Hot algorithm has modest positive effects on both the spread of information and its quality. On complete structures like TikTok, the Hot algorithm leads to a winner-take-all dynamics that has strong negative effects on both information spread and quality, making the relation between content quality and popularity unpredictable. These findings imply that architectural considerations are more powerful levers than algorithmic interventions for the design of healthy online spaces and public discourse. Platform reform efforts focused exclusively on algorithm choice may be insufficient on architecturally unconstrained platforms and unnecessary on architecturally constrained ones.